A Divergence-Based Distance Measure for Intuitionistic Fuzzy Sets and Its Application in the Decision-Making of Innovation Management

Abstract

The theory of intuitionistic fuzzy set has attracted much attention because of its stronger ability in depicting and modeling uncertainty. Recent years, numbers of distance measures of intuitionistic fuzzy sets have been proposed to distinguish the information conveyed by intuitionistic fuzzy sets. However, many existing distance measures cannot meet the requirements of a metric distance. So defining new distance measure for intuitionistic fuzzy sets is important to provide more choice in application. A new method to measure the distance between intuitionistic fuzzy sets is proposed in this paper. The proposed method is developed based on the divergence measure between intuitionistic fuzzy sets, which was firstly introduced by Shannon based on the idea of entropy. The mathematical properties of the new distance measure are discussed, and it is shown that the proposed distance measure satisfies all axiomatic properties of intuitionistic fuzzy distance measure. Numerical examples are presented to verify the effectiveness and reasonability of the new distance measure. Finally, the new distance measure is applied in innovation management to solve the decision making problems. It is illustrated that the proposed distance measure performs better than most of existing measures.